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Which formulas show the relationships between momentum, mass, and velocity? Check all that apply.

A. [tex]p = mv[/tex]
B. [tex]p = \frac{m}{v}[/tex]
C. [tex]p = \frac{v}{m}[/tex]
D. [tex]m = \frac{p}{v}[/tex]
E. [tex]p = \frac{v}{p}[/tex]
F. [tex]v = \frac{p}{m}[/tex]
G. [tex]v = \frac{m}{p}[/tex]

Sagot :

GinnyAnswer
To understand the relationships between momentum (p), mass (m), and velocity (v), let's analyze each formula given:

1. \( p = m v \)
- This is the fundamental formula for momentum. Momentum is defined as the product of mass and velocity.
- This formula is correct.

2. \( p = \frac{m}{v} \)
- This formula suggests that momentum is equal to the mass divided by the velocity.
- This does not align with the fundamental definition of momentum.
- This formula is incorrect.

3. \( p = \frac{v}{m} \)
- This formula suggests that momentum is equal to the velocity divided by the mass.
- This also does not correspond to the basic definition of momentum.
- This formula is incorrect.

4. \( m = \frac{p}{v} \)
- This can be derived from the fundamental formula \( p = m v \).
- Rearranging for \( m \) gives \( m = \frac{p}{v} \).
- This formula is correct.

5. \( p = \frac{v}{p} \)
- This implies that momentum is equal to velocity divided by momentum, which is nonsensical in the context of units and the definition of momentum.
- This formula is incorrect.

6. \( v = \frac{p}{m} \)
- This can also be derived from \( p = m v \).
- Rearranging for \( v \) gives \( v = \frac{p}{m} \).
- This formula is correct.

7. \( v = \frac{m}{p} \)
- This formula suggests that velocity is equal to mass divided by momentum, which is not consistent with the fundamental relationship of momentum.
- This formula is incorrect.

So, the formulas that show the correct relationships between momentum, mass, and velocity are:

1. \( p = m v \)
2. \( m = \frac{p}{v} \)
3. \( v = \frac{p}{m} \)

These three formulas correctly express the relationships between the variables based on the fundamental definition of momentum.
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